Some people prefer to put their baby on while they’re still in the car. I think this is easier if you have a minivan, but it’s doable in a car or SUV, depending on how many free seats you have. I personally find it easiest to put the carrier on before I leave the house. Throw the RS over your shoulder, put the wrap on as far as you can without the baby, tie the MT waist straps around your waist and toss the shoulder straps over your shoulders, etc. (If you have an onbu, you can’t do this.)
Then, just jimmy everything around and get the baby in when you get to your destination. You’ll probably want to do a bit of readjusting when you stand up. 🙂
I personally prefer to stand outside the car to put a baby in the carrier, or carry baby and carrier inside the store and do it there (if it’s raining, snowing, freezing, or hotter than hades). I just don’t have the patience to putz with a carrier and a wiggly baby or toddler INSIDE the car.
As for putting a sling on in public…just pretend that you don’t notice the stares. Keep in mind that people watching are generally being admiring, not critical, and they think you’re wonderfully skilled, even if you feel awkward.